CN114611293B - Method for calculating tunnel structure load in landslide body by combining transfer coefficient method - Google Patents
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Abstract
The invention discloses a method for calculating tunnel structure load in a landslide body by combining a transfer coefficient method, which comprises the following steps: (1) Firstly, calculating the surrounding rock pressure value of a tunnel structure under the conventional condition; (2) Determining the residual sliding force and the residual anti-sliding force of the sliding slope by a transfer coefficient method; according to the assumption of the transfer coefficient method, the landslide section force always acts on the tunnel structure in a direction parallel to the sliding surface. The method improves the problem that the tunnel in the landslide body lacks load theoretical analysis to a great extent, calculates landslide thrust by utilizing a transfer coefficient method aiming at the geometric relationship that the tunnel axial direction is orthogonal to the sliding direction of the landslide and the tunnel is positioned above the sliding surface, and introduces the residual anti-sliding force concept proposed in landslide treatment to calculate the load on the far mountain side of the tunnel. The invention can approximately calculate the thrust load of the landslide born by the tunnel in the landslide body, and provides a new calculation method for the design and reinforcement of the tunnel structure.
Description
Technical Field
The invention relates to the field of tunnel-landslide interaction research, in particular to a method for calculating a tunnel structure load in a landslide body.
Background
More and more tunnels are built in landslide or potential landslide bodies at present, and aiming at the condition that the axial direction of the tunnel and the sliding direction of the landslide are in an orthogonal geometric position relationship, the highway tunnel design rule only carries out a main calculation method on a conventional load, and the special load of landslide thrust is not considered. In addition, the current research on a tunnel landslide system lacks a theoretical calculation method for the stress of the tunnel structure, and a numerical simulation method is adopted to analyze the stress of the tunnel structure.
Disclosure of Invention
Under the condition, the invention provides a theoretical calculation method for the stress of the tunnel supporting structure under the condition of tunnel landslide orthogonality, and the load born by the tunnel structure is calculated by combining the landslide thrust calculated by a transmission coefficient method of the tunnel structure in the landslide body with the Pu's balance arch theory.
The conventional landslide thrust distribution form is generally triangular, rectangular and trapezoidal, and the invention adopts triangular distribution according with practical conditions, so that the landslide thrust acting on a tunnel structure is considered as triangular load.
(1) Firstly, calculating the surrounding rock pressure value of the tunnel structure under the conventional condition. It is assumed that the tunnel structure forms a pressure balance arch as shown in fig. 1. Assuming that a point Q (x, y) is taken, the parabolic equation is obtained according to the Pu's theory as follows:
wherein: uniform load (kN/m) generated by dead weight of rock mass at upper part of q-arch axis 2 ) The method comprises the steps of carrying out a first treatment on the surface of the T-horizontal thrust (kN) of the pressure arch dome cross section; x-coordinate values of any point Q of the x-balance arch parabola; y-y coordinate value of any point Q of the parabola of the balance arch.
When the side wall of the balance arch is stable after the tunnel is deformed, the maximum height of the axis of the balance arch is
b 1 -maximum height (m) of the balancing arch axis; a, a 1 -natural balancing of the maximum span (m) of the arch axis; f-Prussian empirical coefficients related to the integrity of the rock mass and the groundwater;
according to the Rankine soil pressure theory, the angle between the fracture surface and the vertical included angle is as follows:
wherein:
thus, when the equilibrium arch sidewall is unstable, the arch continues to collapse, at which point the maximum span of the natural equilibrium arch axis:
wherein: a-span (m) of the balance arch when the side wall is stable; h-tunnel height (m);-internal friction angle of bulk (°);
from the formula (1) -formula (5):
the tunnel distance from the Q point to the lower part of the Q point is as follows:
at this time, it can be obtained that the vertical load that receives at tunnel supporting construction department below Q point is:
wherein: weighted weight average (kN/m) of loose rock mass between tunnels below gamma-Q point distance 3 )。
To obtain the overall load of the tunnel vault, the integral is carried out to obtain:
the lateral surrounding rock pressure born by the tunnel side wall is calculated by Rankine soil pressure:
wherein: e, e 1 -minimum value above trapezoidal load to which the tunnel side wall is subjected; e, e 2 -maximum value under trapezoidal load applied to the tunnel side wall; p (P) h -all lateral surrounding rock pressure to which the tunnel side wall is subjected.
(2) Determination of the remaining slip force P of a slip by means of a transmission coefficient method i With residual anti-slip force F i :
The transfer coefficient method belongs to a rigid body limit balance analysis method, and is generally divided into an intensity reserve method and an overload method, and belongs to a rigid body limit balance analysis method. The least favorable cross section of the tunnel-landslide system is considered when using the transfer coefficient method and is reduced to the plane strain problem. The assumption conditions for the transfer coefficient method are as follows:
(1) Regarding landslide stability as a plane strain problem;
(2) The sliding force acts on the sliding surface in a concentrated manner by a shearing stress parallel to the sliding surface and a positive stress perpendicular to the sliding surface;
(3) Considering the landslide body as an ideal rigid plastic material, the landslide body is considered to be free from any deformation in the whole loading process, and once the shearing stress along the sliding surface reaches the shearing strength, the landslide body begins to generate shearing deformation along the sliding surface;
(4) The failure of the sliding surface obeys the moire-coulomb failure criterion;
(5) The direction of the residual sliding force is consistent with the inclination angle of the sliding surface, and the transmitted residual sliding force is 0 when the residual sliding force is negative;
(6) The balance condition of the static force is satisfied along the entire sliding surface, but the torque balance condition is not satisfied.
According to the assumption of the transfer coefficient method, the landslide section force always acts on the tunnel structure in a direction parallel to the sliding surface.
The landslide thrust borne by the near mountain side of the tunnel can be determined through calculation by a conventional transfer coefficient method, reverse solution is adopted according to the transfer coefficient method, and a residual anti-slip force concept corresponding to residual downward slip force is introduced when the load of the tunnel structure in a tunnel landslide system is calculated, so that the stress of the tunnel structure at the far mountain side is calculated. The left sliding resistance is calculated reversely on the lower side of the tunnel in a blocking mode, and the left sliding resistance is calculated on the upper side near the mountain side by adopting the left sliding force, so that the landslide thrust born by the structure near the mountain side of the tunnel and the rock and soil resistance born by the far mountain side can be determined simultaneously. If the residual anti-slip force of the far mountain side block is larger than 0, the tunnel far mountain side arch wall is proved to be subjected to the rock-soil resistance action of the lower side block besides the conventional surrounding rock pressure; if the residual anti-slip force of the far mountain side block is smaller than 0, the fact that the lower side block slides along the landslide body is proved, and the lower side block can be considered to not exert other forces on the tunnel side wall.
P i-1 -i-1 st slide down force (kN);
W i-1 -the weight of the i-1 st slide (kN/m) 3 )；
α i-1 -i-1 th slide slip angle (°);
ψ i-2 -i-2 th slide downslide force transmission coefficient;
-the internal friction angle (°) of the i-1 st slide;
c i-1 -i-1 st slide cohesion (kN);
l i-1 -i-1 th slide land length (m);
residual slip resistance of the lower block:
in particular, when F i+2 When less than or equal to 0, let F i+2 =0, i.e.:
landslide thrust acting within the tunnel structure range is:
decomposing landslide thrust on the right side of the acting tunnel structure according to the horizontal and vertical directions:
the remaining slip resistance of the landslide, which would likely act on the left side of the tunnel structure (if F i-1 > 0) decomposition in horizontal and vertical direction:
therefore, after the residual sliding thrust calculated by a transfer coefficient method is considered on the basis of the conventional surrounding rock pressure calculated by the Pursh arch theory, the horizontal resultant force on the right side of the tunnel structure is as follows:
the horizontal resultant force of the left side of the tunnel structure is as follows:
when F i+2 At > 0: q h is left ＝P h +q h2 (25)
When F i+2 When the temperature is less than or equal to 0: q h is left ＝P h (26)
The arch vertical resultant force is:
the present invention has those technical effects compared with the prior art, and the following description is made in connection with the technical advantages of the present invention.
The method improves the problem that the tunnel in the landslide body lacks load theoretical analysis to a great extent, calculates landslide thrust by utilizing a transfer coefficient method aiming at the geometric relationship that the tunnel axial direction is orthogonal to the sliding direction of the landslide and the tunnel is positioned above the sliding surface, and introduces the residual anti-sliding force concept proposed in landslide treatment to calculate the load on the far mountain side of the tunnel. The invention finally provides a unified calculation theory, can approximately calculate the thrust load of the landslide born by the tunnel in the landslide body, and provides a new calculation method for the design and reinforcement of the tunnel structure.
Drawings
Fig. 1 is a schematic diagram of tunnel lining stress in a landslide body according to the present invention.
Fig. 2 is a schematic diagram showing the stress decomposition of a tunnel lining in a landslide body according to the present invention.
FIG. 3 is a schematic representation of a surrounding rock Prussian pressure arch.
FIG. 4 is a schematic diagram of the transfer coefficient method for calculating the sliding force of each block.
Fig. 5 is an explanatory diagram of each geometrical parameter in the present invention.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples.
The invention takes a landslide occurring in the south-end large pond bay of Guangxi resource county of 6 months in 1993 as a calculation case. Through investigation, the area of the landslide sliding body is 1700m 2 Volume of about 6800m 3 . The sliding body mainly comprises granite total weathering layer, conglomerate total weathering layer, residual slope laminated coarse sand, gravel sand and gravel soil. For the calculated load born by the tunnel lining structure in the sliding body, the surrounding rock pressure and the landslide thrust born by the sliding body are required to be calculated respectively and overlapped to obtain an equivalent load, as shown in fig. 1 and 2.
According to the calculation step of the invention, step 1, firstly, the surrounding rock pressure value born by a tunnel with a certain burial depth is calculated according to the Pursh arch theory, and the parameter description is shown in figure 3. According to the on-site survey data of the project, the corresponding parameters are as follows:
table 1 list of calculated parameters
Table1 Table of calculation parameters
Assuming that the tunnel structure is positioned in the 4 th calculation block, substituting the parameters into the parameters (9) and (12) to calculate the vertical load P born by the tunnel v And a horizontal load p h 4.130 KN and 248.5KN respectively.
And 2, slitting the landslide body, and calculating by using transfer coefficients (13) and (15) to obtain the residual sliding force and the residual anti-sliding force of each calculated sliver, wherein the residual sliding force and the residual anti-sliding force are shown in fig. 4. Since the tunnel structure is located in the 4 th calculation bar, the remaining slip force from the upper 3 rd bar, p3, is 473.327KN and the remaining slip force of the lower 5 th bar is 43.090KN. The remaining slip force and the remaining slip resistance calculation results of each bar are shown in table 2.
Table 2 landslide thrust calculation results
Table2 Calculation results
Step 3, substituting the calculation results in Table 2 into the calculation results (19) - (22) according to the calculation diagram in FIG. 5 to obtain the equivalent vertical load q of the tunnel structure under the action of the remaining sliding force of the upper 3 rd block v1 And equivalent horizontal load q h1 Equivalent vertical load q of 944 KN and 56 365KN of tunnel structure under the action of residual anti-slip force of 5 th strip at lower side v2 And equivalent horizontal load q h2 121 800KN and 408 160KN.
Step 4, substituting the calculation results into the steps (23), (24) and (26), and superposing the load generated by landslide thrust and surrounding rock pressure to obtain a horizontal load q borne by the left side of the tunnel structure h is left And the right side bears the horizontal load q h right 56 613KN and 40 840KN. The arch of the tunnel structure bears the vertical load q v The calculation result was 827 300KN.
Claims (1)
1. A method for calculating the load of a tunnel structure in a landslide body by combining a transfer coefficient method comprises the steps of calculating the load born by the tunnel structure by combining landslide thrust calculated by the transfer coefficient method with a Pu's balance arch theory; adopting triangular distribution, and considering landslide thrust acting on a tunnel structure by triangular load; the method is characterized in that: the implementation process of the method is as follows:
(1) Firstly, calculating the surrounding rock pressure value born by a tunnel structure; taking a point Q (x, y), and obtaining a parabolic equation of the point Q (x, y) according to the Pu's theory due to the stress balance of the point on the balance pressure arch:
wherein: the self weight of the rock mass at the upper part of the q-arch axis generates uniform load; t-balancing the horizontal thrust of the arch crown section of the pressure arch; x-coordinate values of any point Q of the x-balance arch parabola; y-the y coordinate value of any point Q of the parabola of the y-balance arch;
when the side wall of the balance arch is stable after the tunnel is deformed, the maximum height of the axis of the balance arch is
b 1 -the maximum height of the balancing arch axis; a, a 1 -natural balancing of the maximum span of the arch axis; f-Prussian empirical coefficients related to the integrity of the rock mass and the groundwater;
according to the Rankine soil pressure theory, the angle between the fracture surface and the vertical included angle is as follows:
wherein:
when the side wall of the balance arch is unstable, the arch is continuously collapsed, and the maximum span of the axis of the natural balance arch is:
wherein: a, the span of the balance arch when the side wall is stable; h-tunnel height;-internal friction angle of the loose mass;
from the formula (1) -formula (5):
the tunnel distance from the Q point to the lower part of the Q point is as follows:
at this time, it is obtained that the vertical load born by the tunnel supporting structure below the Q point is:
wherein: a weighted weight average of loose rock mass between tunnels below the gamma-Q point distance;
in order to obtain the whole load born by the tunnel vault, integration is carried out to obtain:
the lateral surrounding rock pressure born by the tunnel side wall is calculated by Rankine soil pressure:
wherein: e, e 1 -minimum value above trapezoidal load to which the tunnel side wall is subjected; e, e 2 -maximum value under trapezoidal load applied to the tunnel side wall; p (P) h -all lateral surrounding rock pressure to which the tunnel side wall is subjected;
(2) Determination of the remaining slip force P of a slip by means of a transmission coefficient method i With residual anti-slip force F i :
When the transfer coefficient method is used, the least favorable section of a tunnel-landslide system is considered, and the problem of plane strain is simplified; according to the assumption of a transfer coefficient method, the action force between the landslide blocks always acts on the tunnel structure in a direction parallel to the sliding surface;
the method comprises the steps that the left anti-slip force is calculated reversely on the lower side of a tunnel in a blocking mode, the left slip force is calculated on the upper side close to the mountain side by adopting the left slip force, and the landslide thrust force born by the structure close to the mountain side of the tunnel and the rock and soil resistance born by the far mountain side of the tunnel can be determined simultaneously; if the residual anti-slip force of the far mountain side block is larger than 0, the tunnel far mountain side arch wall is proved to be subjected to the rock-soil resistance action of the lower side block besides the conventional surrounding rock pressure; if the residual anti-slip force of the far mountain side block is smaller than 0, proving that the lower side block slides along the landslide body, and considering that no other force is generated on the tunnel side wall;
P i-1 -i-1 st slide down force;
W i-1 -the dead weight of the i-1 th slide;
α i-1 -i-1 st slide slip angle;
ψ i-2 -i-2 th slide downslide force transmission coefficient;
-i-1 th internal friction angle of the slide;
c i-1 -i-1 st slip cohesion;
l i-1 -i-1 th slide face length;
residual slip resistance of the lower block:
in particular, when F i+2 When less than or equal to 0, let F i+2 =0, i.e.:
landslide thrust acting within the tunnel structure range is:
decomposing landslide thrust on the right side of the acting tunnel structure according to the horizontal and vertical directions:
the residual landslide resistance force which possibly acts on the left side of the tunnel structure is decomposed in the horizontal and vertical directions:
and (3) considering the residual sliding thrust calculated by a transfer coefficient method on the basis of the conventional surrounding rock pressure calculated by the Pursh arch theory, wherein the horizontal resultant force on the right side of the tunnel structure is as follows:
the horizontal resultant force of the left side of the tunnel structure is as follows:
when F i+2 >At 0: q h is left ＝P h +q h2 (25)
When F i+2 When the temperature is less than or equal to 0: q h is left ＝P h (26)
The arch vertical resultant force is:
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